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# Frequency Distribution Table Examples for Grouped & Ungrouped Data

12 October,2018

Think about the following situation. You open your lunch box, and you see the same veggies that you had yesterday, the day before yesterday and the day before that as well. You complain to your mom about having the same lunch every day, but in vain. What you do is that you decide to show your mom how many days you had veggies in a month for lunch.

This is where you make a frequency distribution table as it helps you to organize the data, i.e. get a graphical representation of any sample. You can easily find out how many times you had veggies in your lunch and show the result to your mom.

A frequency distribution table is an integral part of statistics. You need to understand the basics of a frequency distribution table before you can take a step forward in solving the sums in statistics.

## What is a frequency distribution table?

A frequency distribution table is a chart that represents values of any given sample and their frequency, i.e. the number of times the values have occurred. Through a frequency distribution table, you can easily handle the outcome of a sample through a proper organization of data.

A frequency distribution table consists of two columns: Column A and Column B. Column A lists the different values of outcomes in a given sample. Column B states the frequency of the outcomes.

## Frequency Distribution Example – Here is the full Concept

An example is the best way to understand a concept. Therefore, let us understand the concept of frequency distribution and the table with an example.

Suppose, you had veggies on 1st, 2nd, 4th, 6th, 7th, 8th, 11th, 13th, 14th, 17th, 19th, 20th, 22th, 25th, 27th, 29th, 30th of a month for lunch. On 3rd, 9th, 12th, 16th, 23rd, you had a hamburger. The rest of the days, i.e. 5th, 10th, 15th, 18th you had chicken dumpling and on 21st, 24th, 26th, 28th, you had eggs.

Now you can represent this data through a frequency distribution table.

 Column A (types on lunch) Column B (no. of days) Veggies 17 Hamburger 5 Chicken dumpling 4 Eggs 4

Study the frequency table example which shows you the number of days you had veggies. Therefore, you can now tell your mom that you had veggies seventeen days of the month.

## What are the different types of frequency distribution?

There are five types of frequency distribution:

• Grouped frequency distribution
• Ungrouped frequency distribution
• Cumulative frequency distribution
• Relative frequency distribution
• Relative cumulative frequency distribution

Each of these types has their own frequency distribution tables. However, in this blog, we will understand what a grouped and ungrouped frequency distribution is along with respective frequency table examples.

## What is grouped and ungrouped data?

Before we understand the grouped and ungrouped frequency distribution, we need to understand what grouped and ungrouped data is.

In simple terms, ungrouped data is raw data that has not been placed in any category. This implies that the data is not given any characteristics. For example, you know that 350 people are living in your area. This is raw data and is not grouped, i.e. divided into any category.

The moment this raw data is categorized, it becomes grouped data. For example, there are 50 children and 300 adults. This data is now organized as you have clear information about the number of children and adults present in your locality.

However, this data can further be classified according to the requirement.

## Ungrouped Frequency Distribution Table with Example

Now, that we have understood the difference between ungrouped and grouped data, it will be easy for us to understand an ungrouped frequency distribution table.

For example, we are assuming the marks that 30 students scored in English, considering the total marks to be 50.

45, 34, 39, 23, 36, 47, 48, 34, 28, 44, 45, 43, 32, 39, 41, 38, 44, 37, 33, 38, 46, 44, 49, 43, 28, 36, 33, 32, 39, 42

Now let us make a table and see how many students got each of these marks.

 Marks Frequency (no. of students) 23 1 28 2 32 2 33 2 34 2 36 2 37 1 38 2 39 3 41 1 42 1 43 2 44 3 45 2 46 1 47 1 48 1 49 1

This is an ungrouped frequency distribution table because we are considering the individual marks are checking how many children got them.

## Grouped Frequency Distribution Table with Example

The above data can be represented in groups as well. Therefore, the next table is a grouped frequency distribution table. The groups are commonly known as class intervals. You might get the class intervals given in the question, or you have to find it yourself.

 Marks Frequency (no. of students) 0 – 10 0 10 – 20 0 20 – 30 3 30 – 40 14 40 – 50 13

The ‘marks’ column is the class interval. A class interval in a grouped frequency distribution table has a lower limit and an upper limit. Therefore, if we take the class interval 20 – 30, 20 is lower limit, and 30 is the upper limit.

However, this grouped frequency table represents the exclusive form of data. This means the class intervals include the lower limit and exclude the upper limit. Therefore, the class interval 20 – 30 will have values starting from 20 – 30.

This type of grouped frequency table is confusing for most students, and sometimes the collected data is not accurately analyzed. To eliminate the confusion, we can represent the grouped frequency distribution data in its inclusive form. This is where the class interval changes.

Let us take the same data and form a grouped frequency distribution table with an inclusive form of data.

 Marks Frequency (no. of students) 0 – 10 0 11 – 20 0 21 – 30 3 31 – 40 14 41 – 50 13

Notice the changes that are made in column A (marks). Therefore, if a certain sum has values like 10, 20, 30, 40, etc. you can easily understand where to put the frequency when you are making a grouped frequency distribution table.

Hence, to conclude, the concept of a frequency distribution is clearly explained along with two different tables and examples. When you know the basic concept clearly, you will easily understand different types of frequency distribution table.

## Cumulative Frequency Distribution

The cumulative frequency distribution is undeniably one of the most important frequency distribution. In this particular form of frequency distribution table, the frequencies are cited in a cumulative format. Here’s how to calculate and define the cumulative frequency distribution of a given set of data.

• The cumulative frequency for each class interval can be derived based on the frequency for that interval, added to the preceding cumulative total.
• Another way to define cumulative frequency is by summing up all previous frequencies up to the current point.

Well, here’s an example for further insights.

For instance, a manager of a grocery store who wants to know how many people spend more than \$3001 in shopping for groceries, the cumulative frequency distribution table should be like this.

### Cumulative Frequency Distribution Table Example

 Type Frequency Cumulative Frequency Up to 1000 22 767 1001 – 2000 45 745 2001 – 3000 57 700 3001 – 4000 97 643 4001 – 5000 152 546 5001 – 6000 241 394

## Relative Frequency Distribution

Study.com defines Relative frequency distribution table as a chart that displays the popularity or mode of a particular type of data, based on the sampled population. The table will help you to develop an idea about the frequency of times a particular event occurs, compared to the entire count of events. It is also to be noted that determining the Relative Frequency Distribution of a particular set of data is all about the percentages, rather than the counts.

Here’s how you should calculate the relative frequency of a class. Look at the images carefully in order to develop further insights.

Available information:

 Frequency Distribution of prices for 20 Gas station Gas Prices (\$/Gallon) Number of Gas stations \$3.50-\$3.74 6 \$3.75-\$3.99 4 \$4.00-\$4.24 5 \$4.25-\$4.49 5

Based on the aforementioned information, the next table shows the relative frequency of the prices in every individual class. Here’s an image explaining the same. Take a look.

 Gas Prices(\$/Gallon) Number of Gas Stations Relative Frequency Relative Frequency (fraction) (percent) \$3.50-\$3.74 6 6/20 = 0.30 30% \$3.75-\$3.99 4 6/20 = 0.30 20% \$4.00-\$4.24 5 6/20 = 0.30 25% \$4.25-\$4.49 5 6/20 = 0.30 25%

We can see that the relative frequency of each class is equivalent to the actual number of gas stations, divided by 20. The result is eventually derived in the form of fractions and percentages.  One significant aspect of using the relative frequency distribution table is the advantage of comparing data sets that don’t contain an equal number of observations.

## Relative Cumulative Frequency Distribution

The relative cumulative frequency is the result that we get after dividing the cumulative frequency by the total frequency. For example, a group of 19 people was asked how many miles, to the nearest miles they commute to reach their workplace every day. Here is a given set of data.

2; 5; 7; 3; 2; 10; 18; 15; 20; 7; 10; 18; 5; 12; 13; 12; 4; 5; 10

Here’s the table that was created in order to explain the frequency distribution. Take note.

 DATA FREQUENCY RELATIVE FREQUENCY CUMULATIVE RELATIVE FREQUENCY 3 3 3/19 0.1579 4 1 1/19 0.2105 5 3 3/19 0.1579 7 2 2/19 0.2632 10 3 4/19 0.4737 12 2 2/19 0.7895 13 1 1/19 0.8421 15 1 1/19 0.8948 18 1 1/19 0.9474 20 1 1/19 1.0000

Now, you must wonder if the table is correct. If not, then what is wrong with it? To answer this question, allow me to tell you that the table is made using an incorrect format. The frequency column should sum up to 19, and not 18. The cumulative frequency column mentioned in the table should read:

 CUMULATIVE RELATIVE FREQUENCY 0.1052 0.1597 0.2105 0.3684 0.4737 0.6316 0.7368 0.7895 0.8421 0.9474 1.0000

Time for Brainstorming! Now that you have every possible idea about the rectified version of the table, spend time exploring the fundamentals based on which the correct table has been created.

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#### Q. What is a Frequency Distribution?

Frequency distribution can be defined as the list, graph or table that is able to display frequency of the different outcomes that are a part of the sample. Each of the entries that are made in the table are based on the count or frequency of occurrences of the values within the particular interval or group. The table mainly summarizes distribution of the values in a sample. Frequency table is able to depict the summarized group of data that is mainly divided based on the mutually exclusive classes and frequency of the occurrences.

#### Q. What are the three types of frequency distribution?

The three major types of frequency distribution are grouped frequency distribution, ungrouped frequency distribution and cumulative frequency distribution. Grouped frequency distribution is considered to be an ordered list of the variable X that is divided into the groups of a single column that has a listing in the second column. Ungrouped frequency distribution is based on an interval width of 1 that is mainly called the ungrouped distribution of frequency. The observed values are thereby distributed in an ascending order. Cumulative frequency distribution is a major type of frequency distribution in which the frequencies are mainly shown in an ascending order.

#### Q. When would you use a frequency table?

The frequency table is mainly used for the purpose of constructing the collected data or values in the ascending order based on the corresponding frequencies and their magnitude. The usage of a frequency table is mainly based on the ways by which different data values can be arranged in an effective manner. The frequency table is able to play a major role in the proper analysis of the data values.

#### Q. What are the characteristics of frequency distribution?

The major characteristics of the frequency distribution table is mainly based on the major factors that include, measuring the central tendency and the location, measuring the levels of dispersion and measuring the extent and level of symmetry.

#### Q. What is the frequency table used for?

A frequency table is mainly used for the purpose of keeping a tally of the ways by which certain events can occur. The tally is mainly based on the running total of the values that have been mainly considered. The frequency tables are considered to be useful for keeping the proper track of the number of times a particular event occurs within a stipulated period of time.

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